1. GloJuju’s Chocolate Shop Gloria Zhou & Julia Lieu

2. Business Plan GloJuju’s Chocolate Shop sells chocolate bars. There are two different kinds of chocolate bars: milk chocolate and dark chocolate. Chocolate Bars Milk Chocolate - $3 Dark Chocolate - $5

3. Variables x= # of milk chocolate bars sold y= # of dark chocolate bars sold C= amount of money profited from chocolate sold Constraints I have $100 dollars to spend. I can only acquire 6 dark chocolate bars. From the vendor, milk chocolate bars cost $1.50 and dark chocolate bars cost $2.50. Variables and Constraints

4. After the first 2 dark chocolate bars, I am contracted to purchase at least one dark chocolate bar for every 2 milk chocolate bars purchased. Constraints cont.

5. Cost Function C=3x+5y

6. Equations 1.5x+2.5y ≤ 100 y ≥ 2 x ≥ 0 y ≤ 6 y+2 ≥ 2x

7. Graph Created with: ww.desmos.com/cal culator

8. Algebra 1. y=2 and x=0 (0, 2) 2. y=6 and x=0 (0, 6) 3. y=2 and y+2 = 2x substitution: 2+2 = 2x simplify: 4 = 2x solve: 4/2 = x x = 2 (2, 2) 4. y=6 and 1.5x+2.5y=100 substitution: 1.5x+2.5(6)=100 simplify: 1.5x=85 solve: x = 56.7 (56.7, 6)

9. Algebra cont. 5. 1.5x+2.5y=100 and y+2=2x substitution: y=2x-2 1.5x+2.5(2x-2)=100 1.5+5x-5=100 simplify: 6.5x=105 solve: x=16.2 plug in: 1.5(16.2)+2.5y=100 simplify: 2.5y=75.7 solve: y=30.3 (16.2, 30.3)

10. Possible “Best” Solutions (0, 2) = 0 milk and 2 dark (0, 6) = 0 milk and 6 dark (2, 2) = 2 milk and 2 dark (56.7, 6) = 56 milk and 6 dark (16.2, 30.3) = 16 milk and 30 dark for (56.7, 6) and (16.2, and 30.3) we used the points (56, 6) and (16, 30) because (57, 6) and (16, 30) wouldn’t fall within our shaded region (violates my constraints) & we cannot sell.7,.2, or.3 of a chocolate bar

11. Best Solution C=3x+5y (0, 2) = 3(0)+5(2) = 0+10 = $10 (0, 6) = 3(0)+5(6) = 0+30 = $30 (2, 2) = 3(2)+5(2) = 6+10 = $16 (56, 6) = 3(56)+5(6) = 168+30 = $198 (16, 30) = 3(16)+5(30) = 48+150 = $198 The best solution for our shop would be to buy 56 milk chocolate bars and 6 dark chocolate bars, or 16 milk chocolate bars and 30 dark chocolate bars because it will produce the most profit with our constraints (see calculations above).